"No longer waiting for Godot. It has begun boring and just completed the first segment of tunnel in LA," Musk said.

Musk said in a Bloomberg profile that the company would begin digging in the SpaceX parking lot. The Boring Company, however, will need to secure permits to dig beyond the SpaceX property line.

Musk's ultimate goal is to relieve congestion by building as many as 30 layers of tunnels beneath Interstate 105 in LA. Musk has said that the tunnels will transport cars on an electric skate and could even accommodate a Hyperloop.

Musk said last Monday that he has had "promising conversations" with Los Angeles Mayor Eric Garcetti about the project.

Los Angeles is contemplating the addition of an express train that would travel between Los Angeles International Airport (LAX) and Union Station, a main transit hub that connects LA to distant suburbs east and west of the city. Garcetti said he is considering using Musk's tunnel to support the rail connection.

The SpaceX parking lot is roughly a five-minute drive from LAX, but securing the necessary permits to dig under the freeway will likely take time.

Still, Musk is clearly dead serious about making his tunnel network a reality. But he says it will take some more time before Godot can beat his pet snail, Gary.